Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 2$ and $ KL = 7x - 8$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 2} = {7x - 8}$ Solve for $x$ $ -2x = -6$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({3}) - 2$ $ KL = 7({3}) - 8$ $ JK = 15 - 2$ $ KL = 21 - 8$ $ JK = 13$ $ KL = 13$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {13} + {13}$ $ JL = 26$